Optimal. Leaf size=18 \[ -3+e^{\frac {5 e^4}{x}} (6-3 x) \]
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Rubi [A] time = 0.33, antiderivative size = 17, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 4, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.089, Rules used = {1593, 6688, 12, 2288} \begin {gather*} 3 e^{\frac {5 e^4}{x}} (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {5 e^4+x \log (6-3 x)}{x}} \left (e^4 (10-5 x)+x^2\right )}{(-2+x) x^2} \, dx\\ &=\int \frac {3 e^{\frac {5 e^4}{x}} \left (-10 e^4+5 e^4 x-x^2\right )}{x^2} \, dx\\ &=3 \int \frac {e^{\frac {5 e^4}{x}} \left (-10 e^4+5 e^4 x-x^2\right )}{x^2} \, dx\\ &=3 e^{\frac {5 e^4}{x}} (2-x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.83 \begin {gather*} -3 e^{\frac {5 e^4}{x}} (-2+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 18, normalized size = 1.00 \begin {gather*} e^{\left (\frac {x \log \left (-3 \, x + 6\right ) + 5 \, e^{4}}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 33, normalized size = 1.83 \begin {gather*} 3 \, x {\left (\frac {2 \, e^{\left (\frac {5 \, e^{4}}{x} + 8\right )}}{x} - e^{\left (\frac {5 \, e^{4}}{x} + 8\right )}\right )} e^{\left (-8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.25, size = 15, normalized size = 0.83
method | result | size |
risch | \(\left (-3 x +6\right ) {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{x}}\) | \(15\) |
gosper | \({\mathrm e}^{\frac {x \ln \left (-3 x +6\right )+5 \,{\mathrm e}^{4}}{x}}\) | \(19\) |
norman | \({\mathrm e}^{\frac {x \ln \left (-3 x +6\right )+5 \,{\mathrm e}^{4}}{x}}\) | \(19\) |
default | \(-\frac {3 \,{\mathrm e}^{4} \left (-125 \,{\mathrm e}^{12} \left (\frac {2 \left ({\mathrm e}^{-8}\right )^{2} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{2}} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}+\frac {5 \,{\mathrm e}^{4}}{2}\right )}{25}-\frac {2 \left ({\mathrm e}^{-8}\right )^{2} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}\right )}{25}+\frac {{\mathrm e}^{-8} {\mathrm e}^{-4} \left (-\frac {x \,{\mathrm e}^{-4} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{x}}}{5}-\expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}\right )\right )}{5}\right )+50 \,{\mathrm e}^{8} \left (\frac {{\mathrm e}^{-8} {\mathrm e}^{-4} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{2}} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}+\frac {5 \,{\mathrm e}^{4}}{2}\right )}{5}-\frac {{\mathrm e}^{-8} {\mathrm e}^{-4} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}\right )}{5}\right )+125 \,{\mathrm e}^{12} \left (\frac {{\mathrm e}^{-8} {\mathrm e}^{-4} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{2}} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}+\frac {5 \,{\mathrm e}^{4}}{2}\right )}{5}-\frac {{\mathrm e}^{-8} {\mathrm e}^{-4} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}\right )}{5}\right )-50 \,{\mathrm e}^{8} {\mathrm e}^{-8} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{2}} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}+\frac {5 \,{\mathrm e}^{4}}{2}\right )+20 \,{\mathrm e}^{4} \left (-\frac {{\mathrm e}^{-8} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{x}}}{2}+\frac {5 \,{\mathrm e}^{-4} {\mathrm e}^{\frac {5 \,{\mathrm e}^{4}}{2}} \expIntegralEi \left (1, -\frac {5 \,{\mathrm e}^{4}}{x}+\frac {5 \,{\mathrm e}^{4}}{2}\right )}{4}\right )\right )}{5}\) | \(261\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -3 \, x e^{\left (\frac {5 \, e^{4}}{x}\right )} - 30 \, \int \frac {e^{\left (\frac {5 \, e^{4}}{x} + 4\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int -\frac {{\mathrm {e}}^{\frac {5\,{\mathrm {e}}^4+x\,\ln \left (6-3\,x\right )}{x}}\,\left (x^2-{\mathrm {e}}^4\,\left (5\,x-10\right )\right )}{2\,x^2-x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 23.67, size = 15, normalized size = 0.83 \begin {gather*} e^{\frac {x \log {\left (6 - 3 x \right )} + 5 e^{4}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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